Examveda

The price of diesel is increased by 26%. A person wants to increase his expenditure by 15% only. By what percentage, correct to one decimal place, should he decrease his consumption?

A. 7.2%

B. 6.5%

C. 8.7%

D. 9.5%

Solution(By Examveda Team)

Given:
Percentage increase in the price of diesel = 26%
Percentage increase in total expenditure = 15%
Concept used:
P × C = E
Where P is Price, C is Consumption and E is Expenditure
Calculation:
Let initial price be P1, consumption be C1, and expenditure be E1
P1 × C1 = E1
⇒ $${{\text{C}}_1} = \frac{{{{\text{E}}_1}}}{{{{\text{P}}_1}}}$$
Let new price be P2, new quantity consumed be C2, and new expenditure be E2
P2 = P1 + 26% of P1
⇒ P2 = 1.26P1
E2 = E1 + 15% of E1
⇒ E2= 1.15E1
As, P2 × C2 = E2
⇒ 1.26P1 × C2 = 1.15E1
⇒ C2 = $$\frac{{{\text{1}}{\text{.15}}{{\text{E}}_1}}}{{{\text{1}}{\text{.26}}{{\text{P}}_1}}}$$
⇒ C2 = 0.9126 × $$\frac{{{{\text{E}}_1}}}{{{{\text{P}}_1}}}$$
⇒ C2 = 0.9126C1
Decrease in consumption = C1 - C2
⇒ Decrease in consumption = C1 - 0.9126C1 = 0.0874C1
Percentage decrease in consumption = $$\frac{{{\text{Decrease in consumption}}}}{{{\text{Initial consumption}}}} \times 100$$
⇒ Percentage decrease in consumption = $$\frac{{0.0874{{\text{C}}_1}}}{{{{\text{C}}_1}}} \times 100$$
∴ The percentage decrease in consumption is 8.7% (correct to 1 decimal place)

This Question Belongs to Arithmetic Ability >> Percentage

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